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In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $unconditional\ uniqueness$ that is independent of the length…

Analysis of PDEs · Mathematics 2023-07-24 P. Jameson Graber , Alpár R. Mészáros

The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity…

Probability · Mathematics 2022-08-11 Chenchen Mou , Jianfeng Zhang

The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the…

Optimization and Control · Mathematics 2022-01-19 Joseph Frédéric Bonnans , Justina Gianatti , Laurent Pfeiffer

We analyze a fractional mean field game of controls system, showing existence of solutions when the order of the fractional Laplacian is $s\in(\frac{1}{2},1)$. Here the running cost depends on the distribution $\mu$ of not only the states…

Analysis of PDEs · Mathematics 2025-09-08 P. Jameson Graber , Elizabeth Matter , Jesus Ruiz Bolanos

The objective of this work is to study the existence, uniqueness, and stability of equilibria in mean field games involving a major player and a continuum of minor players over finite intervals of arbitrary length. Following earlier…

Optimization and Control · Mathematics 2025-01-07 Francois Delarue , Chenchen Mou

It is well known that the monotonicity condition, either in Lasry-Lions sense or in displacement sense, is crucial for the global well-posedness of mean field game master equations, as well as for the uniqueness of mean field equilibria and…

Probability · Mathematics 2022-11-24 Chenchen Mou , Jianfeng Zhang

We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company…

Optimization and Control · Mathematics 2026-05-18 Alessandro Calvia , Salvatore Federico , Giorgio Ferrari , Fausto Gozzi

In this manuscript we study the well-posedness of the master equations for mean field games with volatility control. This infinite dimensional PDE is nonlinear with respect to both the first and second-order derivatives of its solution. For…

Analysis of PDEs · Mathematics 2025-03-14 Chenchen Mou , Jianfeng Zhang , Jianjun Zhou

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of…

Optimization and Control · Mathematics 2017-11-07 Piermarco Cannarsa , Rossana Capuani

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

Optimization and Control · Mathematics 2019-02-06 Alekos Cecchin , Paolo Dai Pra , Markus Fischer , Guglielmo Pelino

We consider a mean-field game model where the cost functions depend on a fixed parameter, called \textit{state}, which is unknown to players. Players learn about the state from a a stream of private signals they receive throughout the game.…

Optimization and Control · Mathematics 2024-02-01 Eran Shmaya , Bruno Ziliotto

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with common noises and their corresponding $N$-player games. The theory of mean field game of controls considers a class of mean field games where the…

Optimization and Control · Mathematics 2022-06-13 Min Li , Chenchen Mou , Zhen Wu , Chao Zhou

In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which…

Optimization and Control · Mathematics 2026-03-27 François Delarue , Pierre Lavigne

This paper studies the relation between equilibria in single-period, discrete-time and continuous-time mean field game models. First, for single-period mean field games, we establish the existence of equilibria and then prove the…

Optimization and Control · Mathematics 2024-11-04 Jodi Dianetti , Max Nendel , Ludovic Tangpi , Shichun Wang

The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…

Optimization and Control · Mathematics 2019-03-19 Bruce Hajek , Michael Livesay

In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens…

Analysis of PDEs · Mathematics 2024-03-25 P. Jameson Graber , Alpár R. Mészáros

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…

Analysis of PDEs · Mathematics 2021-11-04 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

This paper establishes the existence of equilibria result of a class of mean field games with singular controls. The interaction takes place through both states and controls. A relaxed solution approach is used. To circumvent the tightness…

Optimization and Control · Mathematics 2022-05-10 Guanxing Fu

In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak…

Probability · Mathematics 2016-07-05 Saran Ahuja

In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an It\^o diffusion via one-sided singular stochastic control, aiming to…

Optimization and Control · Mathematics 2025-05-14 Giorgio Ferrari , Ioannis Tzouanas
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